Polynomial pseudo-random number generator via cyclic phase

Authors:
A. Marchi;A. Liverani;A. Del Giudice
Affiliations:
Catholic University of Sacred Heart, Economics and Business Administration department, 7 Necchi St., 20123 Milan, Italy;Catholic University of Sacred Heart, Economics and Business Administration department, 7 Necchi St., 20123 Milan, Italy;Catholic University of Sacred Heart, Economics and Business Administration department, 7 Necchi St., 20123 Milan, Italy
Venue:
Mathematics and Computers in Simulation
Year:
2009

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Abstract

Fast and reliable pseudo-random number generator (PRNG) is required for simulation and other applications in scientific computing. In this work, a polynomial PRNG algorithm, based on a linear feedback shift register (LFSR) is presented. LFSR generator of order k determines a 2^k-1 cyclic sequence period when the associated polynomial is primitive. The main drawback of this generator is the cyclicality of the shifted binary sequence. A non-linear transformation is proposed, which eliminates the underlying cyclicality and maintains both the characteristics of the original generator and the feedback function. The modified generator assures a good trade off between fastness and reliability and passes both graphical and statistical tests.